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On the Longest Common Rigid Subsequence Problem

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Abstract

The longest common subsequence problem (LCS) and the closest substring problem (CSP) are two models for finding common patterns in strings, and have been studied extensively. Though both LCS and CSP are NP-Hard, they exhibit very different behavior with respect to polynomial time approximation algorithms. While LCS is hard to approximate within n δ for some δ>0, CSP admits a polynomial time approximation scheme. In this paper, we study the longest common rigid subsequence problem (LCRS). This problem shares similarity with both LCS and CSP and has an important application in motif finding in biological sequences. We show that it is NP-hard to approximate LCRS within ratio n δ, for some constant δ>0, where n is the maximum string length. We also show that it is NP-Hard to approximate LCRS within ratio Ω(m), where m is the number of strings.

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Authors and Affiliations

  1. IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA

    Nikhil Bansal

  2. Department of Computer Science, Bar Ilan University, Ramat Gan, 52900, Israel

    Moshe Lewenstein

  3. Department of Computer Science, University of Western Ontario, London, ON, N6A 5B7, Canada

    Bin Ma & Kaizhong Zhang

Authors
  1. Nikhil Bansal
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  2. Moshe Lewenstein
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  3. Bin Ma
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  4. Kaizhong Zhang
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Correspondence to Nikhil Bansal.

Additional information

Some results in this manuscript were previously presented in CPM’05 conference [14].

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Bansal, N., Lewenstein, M., Ma, B. et al. On the Longest Common Rigid Subsequence Problem. Algorithmica 56, 270–280 (2010). https://doi.org/10.1007/s00453-008-9175-1

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